Harvard-MIT: Chain-Chain-Chain Rule (2009 Feb #2)

Let's quickly make sure we know how to apply chainrule multiple times. Your support is truly a huge encouragement.Please take a second to subscribe in order to send us your valuable support and receive notifications for new videos!Every subscriber and every like are wholeheartedly appreciated.

what secret if you finished calculus heck even calculus ab this shouldn't be any hard its logic using the fundamental theorem of calculus and chain rule, novel concepts there are really scary problems much scarier than this.

Would it be possible for you to take a whole test like this, and show it to us ? I think it could be very interesting to see the whole reasoning behind the big test, if you have time/motivation of course

You may be right. I actually considered presenting the solution using u-substitution, but I decided that may be an unnecessary extra step for this particular problem, whose solution is quite easy to guess. However, some viewers may prefer the solution using substitution.

That is essentially exactly what he has done here, with sin(sin(sin(x))) = u and thus du = cos(sin(sin))*cos(sin(x))*cos(x) dx .He merely skipped the part of pointing out what u and du are and jumped forward to the primitive as it was sort of obvious, provided knowledge of the chain rule.